Graduation Year
2024
Date of Submission
4-2024
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematical Sciences
Reader 1
Lenny Fukshansky
Terms of Use & License Information
Rights Information
© 2024 Danzhe Chen
Abstract
This thesis provides a comprehensive exploration of lattice theory, emphasizing its dual significance in both theoretical mathematics and practical applications, particularly within computational complexity and cryptography. The study begins with an in-depth examination of the fundamental properties of lattices and progresses to intricate lattice-based problems such as the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP). These problems are analyzed for their computational depth and linked to the Subset Sum Problem (SSP) to highlight their critical roles in understanding computational hardness. The narrative then transitions to the practical applications of these theories in cryptography, evaluating the shift from traditional cryptosystems like RSA to sophisticated lattice-based alternatives, including the GGH cryptoscheme. This shift is particularly relevant in the context of emerging quantum computing threats, where lattice-based cryptosystems offer a promising frontier for secure communications. Through detailed analysis, this thesis not only advances the academic discussion on lattices but also underscores their crucial impact on the evolution of cryptographic methods, bridging the gap between abstract mathematical concepts and their real-world cryptographic applications.
Recommended Citation
Chen, Danzhe, "Bridging Theory and Application: A Journey from Minkowski's Theorem to GGH Cryptosystems in Lattice Theory" (2024). CMC Senior Theses. 3681.
https://scholarship.claremont.edu/cmc_theses/3681
